Confidence levels, significance levels and critical values

Confidence levels, significance levels and critical values

Lessons

  • 1.
    Using sample data, it is possible to find a Z-score relating to the claim (the test-statistic).

    Significance level

    Confidence Level (1α(1-\alpha)

    Significance Level (α\alpha)

    Critical Value (ZαZ_{\alpha})

    0.90

    0.10

    ?

    0.95

    0.05

    ?

    0.99

    0.01

    ?



    Left Tail Test:

    . Left tail test, confidence levels, significance levels and critical values

    Right Tail Test:

    . Right tail test, confidence levels, significance levels and critical values

    Two tailed Test:

    . Two tail test, confidence levels, significance levels and critical values


  • 2.
    Finding the Critical Value
    With a significance level of α=0.075\alpha =0.075 what is the resulting critical value of:
    a)
    A right-tailed test?

    b)
    A left-tailed test?

    c)
    A two-tailed test?


  • 3.
    Find the critical value from the following confidence levels for a right-tailed test:
    a)
    90% confidence

    b)
    95% confidence

    c)
    99% confidence


  • 4.
    Rejecting or Failing to Reject the Null Hypothesis
    The following Null Hypothesis and Alternative Hypothesis have been derived from a statement:

    H0H_0:
    p0.5p \leq 0.5

    H1H_1:
    pp > 0.5 0.5

    Using a significance level of 0.100.10 (which corresponds to a critical value of Zα=1.28Z_\alpha=1.28), and a Z-score of Z=1.40Z=1.40 relating to our Null Hypothesis;

    Can we reject the Null Hypothesis?

  • 5.
    The following Null Hypothesis and Alternative Hypothesis have been derived from a statement:

    H0H_0:
    μ175lbs\mu \geq 175 lbs

    H1H_1:
    μ\mu < 175lbs 175 lbs

    Using a 95% confidence level and a Z-score of Z=-1.50 relating to our Null Hypothesis;

    Can we reject the Null Hypothesis?

  • 6.
    The following claim is made.

    “70% of Canadians own a pet”.

    Given that the test-statistic is Z=2.75, with a confidence level of 90% what can be said about the proportions of pet owners in Canada?